Question 1

One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to ______.
A) detect mean differences between groups for each criterion variable
B) detect the extent to which two or more predictor variables interact
C) show cause-and-effect because many predictor variables are added
D) all of these

Accepted Answer

Including multiple predictor variables in a regression equation allows for the detection of interactions between those variables. This can provide deeper insights into the relationships between predictor variables and the criterion variable. Option A is incorrect because detecting mean differences between groups is typically done through ANOVA rather than regression analysis. Option C is also incorrect because regression analysis cannot establish cause-and-effect relationships.

Question 2

In a sample of 22 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt= 2.07,then what is the decision for this test at a .05 level of significance? A) X significantly predicts Y. B) X does not significantly predict Y. C) There is not enough information to answer this question.

Accepted Answer

Without any information on the p-value or test statistic, we cannot conclude that X significantly predicts Y at the .05 level of significance. Thus, we fail to reject the null hypothesis and conclude that X does not significantly predict Y.

Question 3

The degrees of freedom associated with residual variation are equal to ______.
A) the number of predictor variables
B) the number of predictor variables minus one
C) n - 1
D) n - 2

Accepted Answer

The degrees of freedom associated with residual variation are equal to the total number of observations minus the number of estimated coefficients. In a simple linear regression model with one predictor variable, there are two estimated coefficients (intercept and slope), so the degrees of freedom for residual variation are n - 2.

Question 4

If the coefficient of determination is .25 and the sum of squares residual is 180,then what is the value of SS_Y? A) 60 B) 180 C) 240 D) 800

Accepted Answer

The coefficient of determination (R^2) is .25, which means that 25% of the variance in the dependent variable is explained by the model. The sum of squares total (SST) can be found by dividing the sum of squares residual (SSR) by 1 - R^2. So, SST = 180 / (1 - .25) = 180 / 0.75 = 240.

Question 5

Which of the following equations is appropriate for a linear regression with three predictor variables? A) = bX + a B) = b₁X₁ + b₂X₂+ a C) = b₁X₁ + b₂X₂ + b₃X₃ + a D) = b₁X₁ + b₂X₂ + b₃X₃ + b₄X₄ + a

Accepted Answer

This equation includes three predictor variables (S1U1B11, S1U1B12, S1U1B13) and a constant (a), making it appropriate for a linear regression with three predictors. The other equations have either only one predictor variable or more than three.

Question 6

Multiple regression is a statistical method that includes ______ predictor variable(s)in the equation of the regression line.
A) zero
B) one
C) two
D) two or more

Accepted Answer

Multiple regression involves combining two or more predictor variables in the equation of the regression line. Therefore, the correct answer is D, "two or more."

Question 7

A researcher computes the following analysis of regression table.Based on the data given,what is the value of the standard error of estimate? (Note: Complete the table first.)

A) 2.24
B) 5.00
C) 5.74
D) 8.49

Accepted Answer

The answer of A researcher computes the following analysis of...

Question 8

In a sample of 28 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt = 4.28,then what is the decision for this test at a .05 level of significance? A) X significantly predicts Y. B) X does not significantly predict Y. C) There is not enough information to answer this question.

Accepted Answer

Given the F statistic (F_obt = 4.28) for a regression analysis with one predictor and 28 participants, if the F value is significant at the .05 level, it indicates that the predictor variable X significantly predicts the outcome variable Y. The exact critical value for significance depends on the degrees of freedom associated with the F distribution for this test, which are determined by the number of predictors and the sample size. However, without the exact degrees of freedom or the critical F value provided, we typically rely on common critical values for interpretation. An F value of 4.28 generally suggests significance in many contexts at the .05 level, leading to the conclusion that X significantly predicts Y.

Question 9

If the coefficient of determination is .12 and SS_Y = 225,then what is the sum of squares regression for an analysis of regression? A) 27 B) 198 C) 225 D) There is not enough information to answer this question.

Accepted Answer

The coefficient of determination (R^2) is .12, which means that 12% of the variance in the dependent variable is explained by the model. Given that the total sum of squares (SST) is 225, the sum of squares regression (SSR) can be found by multiplying the total sum of squares by the coefficient of determination: SSR = R^2 * SST = .12 * 225 = 27.

Question 10

A researcher computes a perfect negative correlation,in which each data point falls exactly on the regression line.In this example,the value of the standard error of estimate will be ______.
A) less than 0
B) greater than 0
C) equal to 0
D) there is not enough information to answer this question

Accepted Answer

Since every data point falls exactly on the regression line, there is no error in the estimate and hence the standard error of estimate will be equal to 0.

Question 11

A researcher computes an analysis of regression in which MS_residual = 0.82.What is the value of s_e in this example? A) 0.67 B) 0.82 C) 0.91 D) there is not enough information to answer this question

Accepted Answer

The standard error of the estimate (s_e) is the square root of the mean square residual (MS_residual). Therefore, s_e = √0.82 ≈ 0.91.

Question 12

If the coefficient of determination is .30 and the sum of squares regression for an analysis of regression is 210,then what is the value of SS_Y? A) 210 B) 300 C) 490 D) 700

Accepted Answer

The coefficient of determination (R²) is the ratio of the sum of squares regression (SSR) to the total sum of squares (SSY). Given R² = 0.30 and SSR = 210, we can find SSY using the formula R² = SSR/SSY. Thus, 0.30 = 210/SSY, which gives SSY = 210/0.30 = 700.

Question 13

What is the computation for the standard error of estimate?
A) the square root of the mean square regression
B) the square root of the mean square residual
C) the mean square regression, squared
D) the mean square residual, squared

Accepted Answer

The standard error of estimate is computed as the square root of the mean square residual. This measures the average deviation between the predicted values and the actual values, and is used to assess the accuracy of predictions made using a regression model.

Question 14

If the coefficient of determination is .32 and SS_Y = 150,then what is the sum of squares residual for an analysis of regression? A) 48 B) 102 C) 150 D) there is not enough information to answer this question

Accepted Answer

The coefficient of determination (R-squared) is equal to the explained variation (SSR) divided by the total variation (SST). R-squared = SSR/SST 0.32 = SSR/(SSR+SSE) where SSE is the sum of squares error or residual. Therefore, SSE = SSR/0.68 We are given that SSR = SS_Y = 150. So, SSE = 150/0.68 = 220.59 (rounded to 2 decimal places) Therefore, the sum of squares residual is approximately 221, which is closest to option B (102).

Question 15

The standard error of estimate is used as a measure of the ______ in predictions using the equation of a regression line.
A) linearity
B) appropriateness
C) accuracy
D) certainty

Accepted Answer

The standard error of estimate measures the accuracy of predictions made using the equation of a regression line. It tells us how far the actual data points are likely to be from the predicted values. Therefore, the correct choice is accuracy.

Question 16

A statistical method that includes two or more predictor variables in the equation of a regression line to predict changes in a criterion variable is called ______.
A) analysis of variance
B) standard error of estimate
C) residual regression
D) multiple regression

Accepted Answer

Multiple regression is the statistical method that includes two or more predictor variables in the equation of a regression line to predict changes in a criterion variable. Option A (analysis of variance) is a statistical method used to test the difference between two or more means. Option B (standard error of estimate) is an estimate of the variation of the dependent variable around the regression line. Option C (residual regression) is not a statistical method.

Question 17

A researcher computes the following analysis of regression table.Based on the data given,what is the decision for this test at a .05 level of significance? (Note: Complete the table first.)

A) X significantly predicts Y.
B) X does not significantly predict Y.
C) There is not enough information to answer this question.

Accepted Answer

The answer of A researcher computes the following analysis of...

Question 18

An estimate of the standard deviation or distance that data points fall from the regression line is measured by the ______.
A) sum of squares
B) standard error of estimate
C) criterion variable
D) predictor variable

Accepted Answer

The standard error of estimate is the measure of the distance that data points deviate from the regression line. The sum of squares measures the total variability in a set of data and is used in calculating the standard error of estimate. The criterion variable is the variable that is being predicted, while the predictor variable is the variable used to make the prediction. Neither of these directly relates to the measurement of the standard deviation of data points from the regression line.

Question 19

The degrees of freedom associated with regression variation are equal to ______.
A) the number of predictor variables
B) the number of predictor variables minus one
C) n - 1
D) n - 2

Accepted Answer

The degrees of freedom associated with regression variation are equal to the number of predictor variables because each predictor variable used in the model consumes one degree of freedom.

Question 20

The predictions made using multiple regression are often more ______ than the predictions made using linear regression with one predictor variable.
A) informative
B) convoluted
C) confounded
D) realistic

Accepted Answer

Multiple regression uses multiple predictor variables, which can provide a more comprehensive understanding of the factors influencing the outcome, making the predictions more informative.

Quiz 16: Linear Regression and Multiple Regression

One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to ______.

In a sample of 22 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt= 2.07,then what is the decision for this test at a .05 level of significance?

The degrees of freedom associated with residual variation are equal to ______.

If the coefficient of determination is .25 and the sum of squares residual is 180,then what is the value of SS_Y?

Which of the following equations is appropriate for a linear regression with three predictor variables?

Multiple regression is a statistical method that includes ______ predictor variable(s) in the equation of the regression line.

A researcher computes the following analysis of regression table.Based on the data given,what is the value of the standard error of estimate? (Note: Complete the table first.)

In a sample of 28 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt = 4.28,then what is the decision for this test at a .05 level of significance?

If the coefficient of determination is .12 and SS_Y = 225,then what is the sum of squares regression for an analysis of regression?

A researcher computes a perfect negative correlation,in which each data point falls exactly on the regression line.In this example,the value of the standard error of estimate will be ______.

A researcher computes an analysis of regression in which MS_residual = 0.82.What is the value of s_e in this example?

If the coefficient of determination is .30 and the sum of squares regression for an analysis of regression is 210,then what is the value of SS_Y?

What is the computation for the standard error of estimate?

If the coefficient of determination is .32 and SS_Y = 150,then what is the sum of squares residual for an analysis of regression?

The standard error of estimate is used as a measure of the ______ in predictions using the equation of a regression line.

A statistical method that includes two or more predictor variables in the equation of a regression line to predict changes in a criterion variable is called ______.

A researcher computes the following analysis of regression table.Based on the data given,what is the decision for this test at a .05 level of significance? (Note: Complete the table first.)

An estimate of the standard deviation or distance that data points fall from the regression line is measured by the ______.

The degrees of freedom associated with regression variation are equal to ______.

The predictions made using multiple regression are often more ______ than the predictions made using linear regression with one predictor variable.

Quiz 16: Linear Regression and Multiple Regression

One key advantage for including multiple predictor variables in the equation of a regression line is that it allows you to ______.

In a sample of 22 participants,suppose we conduct an analysis of regression with one predictor variable.If Fobt = 2.07,then what is the decision for this test at a .05 level of significance?

The degrees of freedom associated with residual variation are equal to ______.

If the coefficient of determination is .25 and the sum of squares residual is 180,then what is the value of SSY?

Which of the following equations is appropriate for a linear regression with three predictor variables?

Multiple regression is a statistical method that includes ______ predictor variable(s) in the equation of the regression line.

A researcher computes the following analysis of regression table.Based on the data given,what is the value of the standard error of estimate? (Note: Complete the table first.)

In a sample of 28 participants,suppose we conduct an analysis of regression with one predictor variable.If Fobt = 4.28,then what is the decision for this test at a .05 level of significance?

If the coefficient of determination is .12 and SSY = 225,then what is the sum of squares regression for an analysis of regression?

A researcher computes a perfect negative correlation,in which each data point falls exactly on the regression line.In this example,the value of the standard error of estimate will be ______.

A researcher computes an analysis of regression in which MSresidual = 0.82.What is the value of se in this example?

If the coefficient of determination is .30 and the sum of squares regression for an analysis of regression is 210,then what is the value of SSY?

What is the computation for the standard error of estimate?

If the coefficient of determination is .32 and SSY = 150,then what is the sum of squares residual for an analysis of regression?

The standard error of estimate is used as a measure of the ______ in predictions using the equation of a regression line.

A statistical method that includes two or more predictor variables in the equation of a regression line to predict changes in a criterion variable is called ______.

A researcher computes the following analysis of regression table.Based on the data given,what is the decision for this test at a .05 level of significance? (Note: Complete the table first.)

An estimate of the standard deviation or distance that data points fall from the regression line is measured by the ______.

The degrees of freedom associated with regression variation are equal to ______.

The predictions made using multiple regression are often more ______ than the predictions made using linear regression with one predictor variable.

In a sample of 22 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt= 2.07,then what is the decision for this test at a .05 level of significance?

If the coefficient of determination is .25 and the sum of squares residual is 180,then what is the value of SS_Y?

In a sample of 28 participants,suppose we conduct an analysis of regression with one predictor variable.If F_obt = 4.28,then what is the decision for this test at a .05 level of significance?

If the coefficient of determination is .12 and SS_Y = 225,then what is the sum of squares regression for an analysis of regression?

A researcher computes an analysis of regression in which MS_residual = 0.82.What is the value of s_e in this example?

If the coefficient of determination is .30 and the sum of squares regression for an analysis of regression is 210,then what is the value of SS_Y?

If the coefficient of determination is .32 and SS_Y = 150,then what is the sum of squares residual for an analysis of regression?